# Lacunary value

In complex analysis, a subfield of mathematics, a **lacunary value** or **gap** of a complex-valued function defined on a subset of the complex plane is a complex number which is not in the image of the function.[1]

More specifically, given a subset *X* of the complex plane **C** and a function *f* : *X* → **C**, a complex number *z* is called a *lacunary value* of *f* if *z* ∉ image(*f*).

Note, for example, that 0 is the only lacunary value of the complex exponential function. The two Picard theorems limit the number of possible lacunary values of certain types of holomorphic functions.

## References

- Clark, Douglas N., ed. (1999),
*Dictionary of Analysis, Calculus, and Differential Equations*, Comprehensive dictionary of mathematics,**1**, CRC Press, pp. 97–98, ISBN 9780849303203.

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